Unfolding plane curves with cusps and nodes
2015 ◽
Vol 145
(1)
◽
pp. 161-174
Keyword(s):
Given an irreducible surface germ (X, 0) ⊂ (ℂ3, 0) with a one-dimensional singular set Σ, we denote by δ1 (X, 0) the delta invariant of a transverse slice. We show that δ1 (X, 0) ≥ m0 (Σ, 0), with equality if and only if (X, 0) admits a corank 1 parametrization f :(ℂ2, 0) → (ℂ3, 0) whose only singularities outside the origin are transverse double points and semi-cubic cuspidal edges. We then use the local Euler obstruction Eu(X, 0) in order to characterize those surfaces that have finite codimension with respect to -equivalence or as a frontal-type singularity.
2009 ◽
Vol 19
(02)
◽
pp. 545-555
◽
Keyword(s):
2000 ◽
Vol 09
(08)
◽
pp. 1085-1126
Keyword(s):
2019 ◽
Vol 28
(01)
◽
pp. 1950015
2014 ◽
Vol 17
(01)
◽
pp. 1450048
◽
Keyword(s):
Keyword(s):
2005 ◽
Vol 07
(05)
◽
pp. 583-596
◽
1908 ◽
Vol 15
(1)
◽
pp. 1-5
1957 ◽
Vol 53
(1)
◽
pp. 43-56
◽
Keyword(s):